If the vertices of Delta PQR are P(3, 10),Q(6 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) To determine the type of triangle,we calculate the lengths of the sides using the distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.$1$

Vedclass · Accepted Answer

an isosceles

Vedclass · Answer

(C) To determine the type of triangle,we calculate the lengths of the sides using the distance formula: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.$1$. Length of $PQ$: $PQ^2 = (3 - 6)^2 + (10 - 5)^2 = (-3)^2 + (5)^2 = 9 + 25 = 34$. So,$PQ = \sqrt{34}$.$2$. Length of $QR$: $QR^2 = (6 - 1)^2 + (5 - 2)^2 = (5)^2 + (3)^2 = 25 + 9 = 34$. So,$QR = \sqrt{34}$.$3$. Length of $PR$: $PR^2 = (3 - 1)^2 + (10 - 2)^2 = (2)^2 + (8)^2 = 4 + 64 = 68$. So,$PR = \sqrt{68}$.Since $PQ = QR = \sqrt{34}$,two sides of the triangle are equal in length.Therefore,$\Delta PQR$ is an isosceles triangle.

If the vertices of $\Delta PQR$ are $P(3, 10)$,$Q(6, 5)$,and $R(1, 2)$,then $\Delta PQR$ is a $\dots$ triangle.

Similar Questions

In $\Delta ABC$,$A-M-B$,$A-N-C$ and $\overline{MN} \parallel \overline{BC}$. If $MN = 3$ and $BC = 7$,then $M$ divides $\overline{AB}$ from $A$ in the ratio.......

If one vertex of a triangle is $(1, 1)$ and the midpoints of the sides through this vertex are $(-1, 2)$ and $(3, 2)$,then find the centroid of the triangle.

State whether the following statement is true or false. Justify your answer.
The points $A(-1, -2)$,$B(4, 3)$,$C(2, 5)$,and $D(-3, 0)$ in that order form a rectangle.

Find the area of the triangle whose vertices are $(-8, 4), (-6, 6)$ and $(-3, 9).$

The distance of the point $P$ on the $X-$axis from $A(11, 12)$ is $13$ units. The coordinates of $P$ are $\ldots \ldots \ldots \ldots$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module