i would like to say that after remembering the Coordinate Geometry formulas you can start the questions and answers solution of the Coordinate Geometry chapter. The main concern of every student about maths subject is the Geometry Formulas. \(\frac{x-x_{1}}{\ell_{1}}=\frac{y-y_{1}}{m_{1}}=\frac{z-z_{1}}{n_{1}} \text { and } \frac{x-x_{2}}{\ell_{2}}=\frac{y-y_{2}}{m_{2}}=\frac{z-z_{2}}{n_{2}}\) The Plane Geometry deals with shapes such as circles, triangles, rectangles, square and more. The equation of the planes bisecting the angles between the planes a1x + b1y + c1z + d1 = 0 and a2x + b2y + c2z + d2 = 0 are If α, β, γ be the angles made by a line with coordinate axes, then direction cosine are l = cos α, m = cos β, n = cos γ and relation between dc’s: l2 + m2 + n2 = 1 i.e. Let the coordinates of L be (x1 + aλ, y1 + bλ, + z1 + cλ). A Greek mathematician Euclid is named as the Father of Geometry and he explained how geometry is useful in understanding a variety of early cultures. There are a variety of coordinate geometry formulas that are used to draw graphs of curves or lines. \(\frac{\left(a_{1} x+b_{1} y+c_{1} z+d_{1}\right)}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}}=\pm \frac{\left(a_{2} x+b_{2} y+c_{2} z+d_{2}\right)}{\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}\) In simple words, geometry is a special branch of mathematics that includes the study of shapes, size, dimensions etc. \(\frac{\ell}{a}=\frac{m}{b}=\frac{n}{c}\) = ± \(\frac{\sqrt{\ell^{2}+m^{2}+n^{2}}}{\sqrt{a^{2}+b^{2}+c^{2}}}=\pm \frac{1}{\sqrt{a^{2}+b^{2}+c^{2}}}\) Summary of Coordinate Geometry Formulas. If the vertices of a triangle are (x1, y1, z1), (x2, y2, z2) and (x3, y3, z3) then Important Formulas: Slope of PQ = m = Equation of PQ is as below: or y = mx + c. The product of the slopes of two perpendicular lines is –1. If Ayz, Azx, Axy be the projection of an area A on the coordinate plane yz, zx and xy respectively then A = \(\sqrt{A_{y z}^{2}+A_{z x}^{2}+A_{x y}^{2}}\) Right Triangle and Pythagora's theorem Pythagora's theorem: The two sides a and b of a right triangle and the hypotenuse c are related by AB || CD ⇔ l1 = l2, m1 = m2, n1 = n2 (x1 + aλ – α) a + (y1 + bλ – β) b + (z1 + cλ – γ) c = 0 = a, b, c dr s ⇔ \(\frac{a}{\ell}=\frac{b}{m}=\frac{c}{n}\) Summary of Coordinate Geometry formulas. The x-axis is the horizontal line and the y-axis is the vertical line. \(\left|\begin{array}{ccc}x_{2}-x_{1} & y_{2}-y_{1} & z_{2}-z_{1} \\\ell_{1} & m_{1} & n_{1} \\\ell_{2} & m_{2} & n_{2}\end{array}\right|\) = 0, Area of a triangle: Note: 18. ∴ S.D. By Mark Ryan . Coordinate Geometry also is known as analytic geometry that describes the link between geometry and algebra using graphs and involving curves and lines. Geometry gives you a perfect idea of measurement too. Perpendicular distance of a point from a line, (a) Cartesian Form: ax2 + by2 + cz2 + 2fyz + 2gzx + 2hxy = 0 is a homogeneous equation of 2nd degree may represent pair of planes if Distance between two points. The next important thing that strikes to learners’ mind is the list of basic geometry formulas. coplanar then \(\left|\begin{array}{ccc}x_{2}-x_{1} & y_{2}-y_{1} & z_{2}-z_{1} \\\ell_{1} & m_{1} & n_{1} \\\ell_{2} & m_{2} & n_{2}\end{array}\right|\) = 0 \(\frac{p-\alpha}{a}=\frac{q-\beta}{b}=\frac{r-\gamma}{c}=\frac{-(a \alpha+b \beta+c \gamma+d)}{a^{2}+b^{2}+c^{2}}\) Not anymore, because we have curated the list of 3-Dimensional Coordinate Geometry formulas on this page. \(\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1\). A coordinate graph consists of a rectangular grid with two crossing lines called axes. We will use the below picture as a reference for the formulas. \ell & m & n\end{array}\right|=0 \text { and }\left|\begin{array}{cccc}x-x_{2} & y-y_{2} & z-z_{2} \\\ell_{2} & m_{2} & n_{2} \\\ell & m & n\end{array}\right|=0\), If the vertices of tetrahedron are (x1, y1, z1), (x2, y2, z2), (x3, y3, z3) and (x4, y4, z4) then